Convergence of Nonlinear Observers on Rn With a Riemannian Metric (Part I) - Mines Paris Accéder directement au contenu
Article Dans Une Revue IEEE Transactions on Automatic Control Année : 2012

Convergence of Nonlinear Observers on Rn With a Riemannian Metric (Part I)

Laurent Praly

Résumé

We study how convergence of an observer whose state lives in a copy of the given system's space can be established using a Riemannian metric. We show that the existence of an observer guaranteeing the property that a Riemannian distance between system and observer solutions is nonincreasing implies that the Lie derivative of the Riemannian metric along the system vector field is conditionally negative. Moreover, we establish that the existence of this metric is related to the observability of the system's linearization along its solutions. Moreover, if the observer has an infinite gain margin then the level sets of the output function are geodesically convex. Conversely, we establish that, if a complete Riemannian metric has a Lie derivative along the system vector field that is conditionally negative and is such that the output function has a monotonicity property, then there exists an observer with an infinite gain margin.

Dates et versions

hal-00722761 , version 1 (03-08-2012)

Identifiants

Citer

Ricardo Sanfelice, Laurent Praly. Convergence of Nonlinear Observers on Rn With a Riemannian Metric (Part I). IEEE Transactions on Automatic Control, 2012, 57 (7), pp.1709-1722. ⟨10.1109/TAC.2011.2179873⟩. ⟨hal-00722761⟩
96 Consultations
1 Téléchargements

Altmetric

Partager

Gmail Facebook Twitter LinkedIn More